Research Article

Students’ computation strategy preferences for multi-digit addition and subtraction problems using a free-choice format

Laura B. Kent 1 *
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1 Associate Professor of Mathematics Education, University of Arkansas, Fayetteville, AR, USA* Corresponding Author
Contemporary Mathematics and Science Education, 4(2), 2023, ep23024, https://doi.org/10.30935/conmaths/13443
Published Online: 23 June 2023, Published: 01 July 2023
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ABSTRACT

This article describes the strategies of 71 students, ages 11-13, to multi-digit addition and subtraction problems using a free-choice format. Students were given the opportunity to solve each task two ways. Results showed that the majority of students converted the equation form of the task to a column method as their first preference. The column method incorporated standard algorithm strategies starting with the ones place and regrouping to higher place values to calculate the value of the unknown. On one of the three tasks, more than half of the students switched to a relational thinking strategy to find the unknown as their second-choice strategy. Less than half of the students used number relationships or equivalence strategies on the other two, more complex tasks for either of the two preferences. The overall preference for column methods as the first strategy choice was consistent across all three tasks.

CITATION (APA)

Kent, L. B. (2023). Students’ computation strategy preferences for multi-digit addition and subtraction problems using a free-choice format. Contemporary Mathematics and Science Education, 4(2), ep23024. https://doi.org/10.30935/conmaths/13443

REFERENCES

  1. Barnett, J. H. (1998). A brief history of algorithms in mathematics. In L. J. Morrow, & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics: 1998 yearbook (pp. 69-77). National Council of Teachers of Mathematics.
  2. Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
  3. Blanton, M. L., & Kaput, J. J. (2017). Building district capacity for teacher development in algebraic reasoning. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 361-388). Routledge. https://doi.org/10.4324/9781315097435-17
  4. Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. M. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102(2), 193-219. https://doi.org/10.1007/s10649-019-09894-7
  5. Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62. https://doi.org/10.2307/749717
  6. Bogdan, R. C., & Biklen, S. (2003). Qualitative research for education: An introduction to theory and methods. Allyn & Bacon.
  7. Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach’ to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM, 43(6), 965-977. https://doi.org/10.1007/s11858-011-0353-2
  8. Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic & algebra in elementary school. Heinemann.
  9. Caviola, S., Mammarella, I. C., Pastore, M., & LeFevre, J. A. (2018). Children’s strategy choices on complex subtraction problems: Individual differences and developmental changes. Frontiers in Psychology, 9, 1-16. https://doi.org/10.3389/fpsyg.2018.01209
  10. Ebby, C. B. (2005). The powers and pitfalls of algorithmic knowledge: A case study. The Journal of Mathematical Behavior, 24(1), 73-87. https://doi.org/10.1016/j.jmathb.2004.12.002
  11. Falkner, K., Levi, L., & Carpenter, T. (1999). Early childhood corner: Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6(4), 232-236. https://doi.org/10.5951/TCM.6.4.0232
  12. Fischer, J. P., Vilette, B., Joffredo-Lebrun, S., Morellato, M., Le Normand, C., Scheibling-Seve, C., & Richard, J. F. (2019). Should we continue to teach standard written algorithms for the arithmetical operations? The example of subtraction. Educational Studies in Mathematics, 101(1), 105-121. https://doi.org/10.1007/s10649-019-09884-9
  13. Fyfe, E. R., Matthews, P. G., Amsel, E., McEldoon, K. L., & McNeil, N. M. (2018). Assessing formal knowledge of math equivalence among algebra and pre-algebra students. Journal of Educational Psychology, 110(1), 87-101. https://doi.org/10.1037/edu0000208
  14. Groves, S., & Stacey, K. (1998). Calculators in primary mathematics: Exploring number before teaching algorithms. In L. J. Morrow, & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics: 1998 yearbook (pp. 120-129). National Council of Teachers of Mathematics.
  15. Hickendorff, M., Torbeyns, J., & Verschaffel, L. (2019). Multi-digit addition, subtraction, multiplication, and division strategies. In A. Fritz, V. G. Haase, & P. Räsänen (Eds.), International handbook of mathematical learning difficulties (pp. 543-560). Springer. https://doi.org/10.1007/978-3-319-97148-3_32
  16. Jóelsdóttir, L. B., & Sunde, P. B. (2022). Calculation methods and arithmetical accuracy from grades 3-8: Algorithmic approaches are less accurate than number-based yet increasingly preferred. In Proceedings of the Mathematical Cognition and Learning Society Conference 2022: Multiple Perspectives on Numerical Cognition and Learning.
  17. Kamii, C. (1994). Young children continue to reinvent arithmetic–3rd grade: Implications of Piaget’s theory. Teachers College Press.
  18. Kamii, C. (1998). The harmful effects of algorithms in grades 1-4. In J. L. Morrow, & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics: 1998 yearbook (pp. 130-140). National Council of Teachers of Mathematics.
  19. Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel? Educational Studies in Mathematics, 105(3), 349-365. https://doi.org/10.1007/s10649-020-09983-y
  20. Knuth, E. J., Alibali, M. W., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2008). The importance of equal sign understanding in the middle grades. Mathematics Teaching in the Middle School, 13(9), 514-519. https://doi.org/10.5951/MTMS.13.9.0514
  21. Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297-312.
  22. Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication. Journal of Experimental Psychology: General, 124(1), 83-97. https://doi.org/10.1037/0096-3445.124.1.83
  23. Lord, E., & Stylianides, A. (2019). Strategy choices and formal algorithms: A mixed methods study. In Proceedings of the 11th Congress of the European Society for Research in Mathematics Education. ERME.
  24. Molina, M., & Ambrose, R. C. (2006). Fostering relational thinking while negotiating the meaning of the equals sign. Teaching Children Mathematics, 13(2), 111-117. https://doi.org/10.5951/TCM.13.2.0111
  25. Stephens, A., Stroud, R., Strachota, S., Stylianou, D., Blanton, M., Knuth, E., & Gardiner, A. (2021). What early algebra knowledge persists 1 year after an elementary grades intervention? Journal for Research in Mathematics Education, 52(3), 332-348. https://doi.org/10.5951/jresematheduc-2020-0304
  26. Torbeyns, J., Peters, G., De Smedt, B., Ghesquière, P., & Verschaffel, L. (2018). Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study. Journal of Numerical Cognition, 4(1), 215-234. https://doi.org/10.5964/jnc.v4i1.77
  27. Van Der Auwera, S., De Smedt, B., Torbeyns, J., Verguts, G., & Verschaffel, L. (2023). Subtraction by addition in young multi-digit subtraction learners: A choice/no-choice study. Journal of Experimental Child Psychology, 226, 1-17. https://doi.org/10.1016/j.jecp.2022.105544
  28. Vermeulen, J. A., Béguin, A., Scheltens, F., & Eggen, T. J. (2020). Diagnostic assessment in third-grade subtraction: The relation between bridging errors, number of errors and mathematical ability. Assessment in Education: Principles, Policy & Practice, 27(6), 687-706. https://doi.org/10.1080/0969594X.2020.1856038